Bunuel
Set S has a range of p and the largest number in set S is v. Set T has a range of q and the largest number in set T and the largest number in set T is w. Is the smallest number in set S greater than the smallest number in set T?
(1) p < q
(2) The median of set S is less than the median of set T, and the average (arithmetic mean) of set S is greater than the mean of set T.
Neither statement nor both statements together are sufficient to determine if the smallest number in set S is greater than the smallest number in set T, because the provided information about the range and the relative values of medians and means is insufficient to make this comparison. For example, even with the conditions in statement (2) met, we can construct scenarios where the smallest number in S is larger or smaller than the smallest in T.
Why Statement (1) is not sufficient:p < q (the range of set S is less than the range of set T). Knowing that S has a smaller range than T, along with the specific largest numbers (v for S and w for T), does not tell us about their respective smallest numbers. It's possible for S to have a smaller range but still contain a large smallest number.
Why Statement (2) is not sufficient:The median of set S is less than the median of set T, and the average (arithmetic mean) of set S is greater than the mean of set T.While this statement provides information about the central tendency and distribution of the sets, it's still not enough to definitively compare the smallest elements. You can have sets with different medians and means where the smallest value in the set with the higher mean is still larger or smaller than the smallest value in the set with the lower mean.
Why Statements (1) and (2) together are not sufficient:Even when combining both conditions, we still cannot find a definitive answer. We would need more information about the number of elements in each set or how those elements are distributed relative to their known ranges and central tendencies.
Source: AI Overview